HMMT 二月 2009 · CALC 赛 · 第 5 题
HMMT February 2009 — CALC Round — Problem 5
题目详情
英文原题
- [ 4 ] Compute
( ) ( ) ( ) ( ) ( )
π π π π πsin + 4 h − 4 sin + 3 h + 6 sin + 2 h − 4 sin + h + sin
3 3 3 3 3
lim .
h → 04 h
解析
英文解析
- [ 4 ] Compute
( ) ( ) ( ) ( ) ( )
π π π π π + 4 h − 4 sin + 3 h + 6 sin + 2 h − 4 sin + h + sinsin
3 3 3 3 3
4 limh → 0
√h
Answer:3
f ( x + h ) − f ( x )2
′
Solution: The derivative of a function is defined as f ( x ) = lim . Iterating thish → 0
formula four times yieldshf ( x + 4 h ) − 4 f ( x + 3 h ) + 6 f ( x + 2 h ) − 4 f ( x + h ) + f ( x )
(4)
f ( x ) = lim .
h → 0 h 4
√